Computation of FREE CONVECTION P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi Quantification of Free …….

Governing Equations Now, we can see buoyancy effects replace pressure gradient in the momentum equation. Strongly coupled and must be solved simultaneously The buoyancy effects are confined to the momentum equation, so the mass and energy equations are the same.

Dimensionless Similarity Parameter The x-momentum and energy equations are

Dimensionless Similarity Parameter Define new dimensionless parameter, forced natural Grashof number in natural convection is analogous to the Reynolds number in forced convection. Grashof number indicates the ratio of the buoyancy force to the viscous force. Higher Gr number means increased natural convection flow

u(x,y) y g x v u Laminar Free Convection on Vertical Surface As y   : u = 0, T = T  As y  0 : u = 0, T = T s With little or no external driving flow, Re  0 and forced convection effects can be safely neglects

Analytical similarity solution for the local Nusselt number in laminar free convection Average Nusselt # = Where

Effects of Turbulence Just like in forced convection flow, hydrodynamic instabilities may result in the flow. For example, illustrated for a heated vertical surface: Define the Rayleigh number for relativemagnitude of buoyancy and viscous forces

Effects of Turbulence Transition to turbulent flow greatly effects heat transfer rate.

Empirical Correlations Typical correlations for heat transfer coefficient developed from experimental data are expressed as: For Turbulent For Laminar

Vertical Plate at constant Ts

Alternative applicable to entire Rayleigh number range (for constant Ts) Vertical Cylinders Use same correlations for vertical flat plate if:

Free Convection from Inclined Plate Cold plate or Hot fluid Hot plate or Cold fluid

Horizontal Plate Cold Plate (Ts < T  ) Hot Plate (Ts > T  ) Active Upper Surface Active Lower Surface

Empirical Correlations : Horizontal Plate Define the characteristic length, L as Upper surface of heated plate, or Lower surface of cooled plate : Lower surface of heated plate, or Upper surface of cooled plate : Note: Use fluid properties at the film temperature

Empirical Correlations : Long Horizontal Cylinder Very common geometry (pipes, wires) For isothermal cylinder surface, use general form equation for computing Nusselt #

Ra D C n Constants for general Nusselt number Equation

free convection turbulent heat transfer in an enclosure Turbulent flow in an enclosed cavity or box is a model for many flows of practical interest: Heating of a room. Flow in a double glazing Window. Spreading of fire and fire generated gases in an building.

Velocity Vectors on A Central Vertical Plane

Isotherms on A Central Vertical Plane

Nusselt Number Correlations Small Window Large Window

Natural Convection in A Pool of Saturated Liquid T sat Onset of Convection T surface

Further Behavior of Saturated Liquid Increasing D T Natural Convection Onset of Boiling Isolated Bubble Regime

High Overshoots !!! Wall Superheat ( D T=T s – T sat ) Heat Flux Overshoot A B A: Onset of Natural convection B: Onset of Nucleate Boiling

BOILING HEAT TRANSFER P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi A Basic means of Power Generation…… A science which made Einstein Very Happy!!!

Boiling In a steam power plant convective heat transfer is used to remove heat from a heat transfer surface. The liquid used for cooling is usually in a compressed state, (that is, a subcooled fluid) at pressures higher than the normal saturation pressure for the given temperature. Under certain conditions some type of boiling can take place. It is an important process in nuclear field when discussing convection heat transfer. More than one type of boiling can take place within a nuclear facility.

Nuclear Power Plant

Steam Boiler

Classification of Boiling Microscopic classification or Boiling Science basis: Nucleated Boiling Bulk Boiling Film Boiling Macroscopic Classification or Boiling Technology basis: Flow Boiling Pool Boiling

Nucleate Boiling The most common type of local boiling encountered in nuclear facilities is nucleate boiling. In nucleate boiling, steam bubbles form at the heat transfer surface and then break away and are carried into the main stream of the fluid. Such movement enhances heat transfer because the heat generated at the surface is carried directly into the fluid stream. In the main fluid stream, the bubbles collapse because the bulk temperature of the fluid is not as high as the heat transfer surface temperature where the bubbles were created. This heat transfer process is sometimes desirable because the energy created at the heat transfer surfa ce is quickly and efficiently "carried" away.

Bulk Boiling As system temperature increases or system pressure drops, the bulk fluid can reach saturation conditions. At this point, the bubbles entering the coolant channel will not collapse. The bubbles will tend to join together and form bigger steam bubbles. This phenomenon is referred to as bulk boiling. Bulk boiling can provide adequate heat transfer provided that the steam bubbles are carried away from the heat transfer surface and the surface is continually wetted with liquid water. When this cannot occur film boiling results.

Film Boiling When the pressure of a system drops or the flow decreases, the bubbles cannot escape as quickly from the heat transfer surface. Likewise, if the temperature of the heat transfer surface is increased, more bubbles are created. As the temperature continues to increase, more bubbles are formed than can be efficiently carried away. The bubbles grow and group together, covering small areas of the heat transfer surface with a film of steam. This is known as partial film boiling. Since steam has a lower convective heat transfer coefficient than water, the steam patches on the heat transfer surface act to insulate the surface making heat transfer more difficult. As the area of the heat transfer surface covered with steam incr eases, the temperature of the surface increases dramatically, while the heat flux from the surfa ce decreases.

This unstable situation continues until the affected surface is covered by a stable blanket of steam, preventing contact between the heat transfer surface and the liquid in the center of the flow channel. The condition after the stable steam blanket has formed is referred to as film boiling. The process of going from nucleate boiling to film boiling is graphically represented in Figure. The figure illustrates the effect of boiling on the relationship between the heat flux and the temperature difference between the heat transfer surface and the fluid passing it.

Boiling Curve